圆形隧道开挖卸荷效应的动静态解析方法及结果分析

DYNAMIC AND STATIC ANALYTICAL METHOD OF EXCAVATION UNLOADING EFFECT IN CIRCULAR TUNNEL AND RESULTS ANALYSIS

针对地下圆形隧道的开挖卸荷效应,基于岩石动力学和弹塑性理论,在求解其动、静态显式解析解方面进行新的尝试。首先,探讨非均匀应力场中圆形隧洞开挖卸荷的力学模型,研究初始应力的分布规律以及卸荷过程的处理方法。基于Laplace变换和留数定理,给出一种计算隧道开挖时围岩响应规律动态解析解的方法,得到线性卸荷条件下围岩应力和位移的解析表达式。其次,考虑岩体的非线性硬化和软化特性,运用弹塑性解析法,推导出围岩应力和位移的静态解析表达式。对比分析动静态解析结果的差异,结果表明:(1)卸载阶段,惯性力的存在能减少开挖卸荷对围岩的破坏,保持围岩的完整性,故而在动态解析结果中,围岩的扰动范围小,位移小,应力集中系数低,但应力梯度较高。(2)动态解中,径向应力一直处于压缩状态,而切向应力先拉后压,有利于径向拉裂纹及层板结构的形成。(3)卸荷速率存在临界值,当卸荷速率达到临界值时,质点的振幅及频率都达到最大值。

An attempt is initiated to obtain the dynamic and static explicit solutions for the unloading effect in underground engineering based on rock dynamics and elastoplastic theory. So, the mechanical model of dynamical excavation in circular tunnel with nonuniform geostress was explored; and the distribution law of initial stress and the processing method for unloading are studied firstly. Based on the Laplace transform and residue theorem, a dynamically analytical method to calculate the behavior of surrounding rock in the condition of excavation is put forward~ and the stress and deformation analytical formula of surrounding rock is obtained under the condition of linear unloading. Then, taking the nonlinear strain hardening and softening properties into account, using elastoplastic analytical method, some analytical expressions for the stress and deformation of surrounding rock arededuced. Comparison between dynamically and statically analytical results is drawn to get the difference. The results show： （1） The existence of inertia force is beneficial to reducing the damage of surrounding rock generated from excavation unloading and maintaining its integrity. Thus, the disturbance scope, deformation and stress concentration factor is relatively smaller while the stress gradient is higher in surrounding rock according to the dynamic results. （2） According to the dynamic results, the radial stress is in compression status all the time, while the tangential stress becomes from tensile stress at first time to high compressive stress, which contributes to the formation of tensile crack in radial direction and sandwich structure. （3） A critical value is found in the unloading rate. It is meant that the vibrating amplitude and frequency of particle reach the maximum when the unloading rate is equal to the critical value.